1. Field of the Invention
This invention relates to a device for the direction-of-arrival (DOA) estimation of a radio wave impinging on an array antenna at a base station with high estimation accuracy and low computational complexity and to a receiving/transmitting device for beamforming at a base station which varies the directivity of beam of an antenna based on the estimated directions. This invention is of a technique by which the directions of incident signals (signals which are not uncorrelated to one another, or the multipath waves which are fully correlated) are estimated in a computationally efficient way and is especially a technique for estimating the directions of closely spaced incident waves with high accuracy even when the length of received data is short (i.e., the number of snapshots) and when the signal-to-noise (SNR) is low.
2. Description of the Relate Art
In recent years, the study and development of adaptive array antenna for mobile communications has gathered interest. In the adaptive array antenna, antenna elements are arrayed with a certain geometry in different spatial positions. A technique for estimating the direction-of-arrival (DOA) of a radio wave (referred to also as a “signal” from the view point of signal processing) impinges on an antenna is an important elemental technique for an adaptive array antenna. For estimating the directions of the incident signals, subspace-based methods which utilize the orthogonality between a signal subspace and a noise subspace are well known due to their high estimation accuracy and relatively low computational complexity, where the eigendecomposition such as eigenvalue decomposition (EVD) of an array covariance matrix or singular value decomposition (SVD) of an array data matrix is required to obtain a signal subspace (or a noise subspace). However, for a real installed array antenna, especially in the case where the number of array elements is larger, the calculation process for the eigendecomposition becomes computationally intensive and time-consuming.
In general, for the problem of estimating the direction-of-arrival of uncorrelated incident waves impinging on an array antenna, subspace-base methods utilizing the orthogonality between a signal subspace and a noise subspace are well known because of their relatively computational simplicity and high resolution, where the MUSIC (Multiple signal classification) is a representative method (for details of this technique, refer to “Multiple emitter location and signal parameter estimation,” by R. O. Schmidt, IEEE Trans. Antennas and Propagation, vol. 34, no. 3, pp. 276–280 (1986)). Furthermore, for estimating the directions of fully correlated signals (i.e., multipath waves), the subspace-based method with spatial smoothing is usually used, for example,the spatial smoothing based MUSIC (for the details of this technique, refer to “On spatial smoothing for direction-of-arrival estimation of coherent signals,” by T. J. Shan, M. Wax and T. Kailath, IEEE Trans. Acoust., Speech, Signal Processing, vol. 33, no. 4, pp. 806–811(1985), and also “Forward/backward spatial smoothing techniques for coherent signals identification,” by S. U. Pillai and B. H. Kwon, IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, no. 1, pp. 8–15 (1989)).
In the conventional subspace-based method for estimating the directions of uncorrelated signals, the signal subspace or noise subspace is obtained by the eigenvalue decomposition of the array covariance matrix. Then, the directions of incident signals are estimated by utilizing the orthogonality between the signal subspace and the noise subspace. However, for the direction estimation of the correlated signals (including the fully correlated signals), a uniform linear array (ULA) is usually divided into subarrays in order to suppress the coherency between incident signals and to restore the dimension of the signal subspace of the spatially averaged covariance matrix to the number of the incident signals. Accordingly, the direction estimation of the correlated signals is realized by utilizing the orthogonality between the signal subspace and the noise subspace similarly to the conventional subspace-based method.
In order to explain a demerit of the conventional subspace-based method for the direction estimation of correlated signals, the spatial smoothing based MUSIC is briefly explained as is discussed in an exemplary document “On spatial smoothing for direction-of-arrival estimation of coherent signals,” by T. J. Shan, M. Wax and T. Kailath, IEEE Trans. Acoust., Speech, Signal Processing, vol. 33, no. 4, pp. 806–811 (1985).
Here, it is assumed that p narrow band signals {sk(n)} impinge on a uniform linear array consisting of M array elements from angles {θk} (where k=1 to p). The array received signal for each element can be expressed asy(n)=[y1(n),y2(n), . . . , yM(n)]T=As(n)+w(n)  [Equation 1]where A=[a(θ1),a(θ2), . . . , a(θp)], a(θk)=[l,ejω0 r(θk), . . . , ejω0(M−1)r(θk)]T, s(n)=[s1(n),s2(n), . . . ,sp(n)]T, w(n)=[w1(n),w2(n), . . . , wM(n)]T, ω0=2πf0, τ(θk)=(d/c)sin θk. And f0 is a carrier frequency, c is a propagation speed, and d is element spacing. Also, (•)T means a transpose, a (θk) and A are respectively a response vector and a response matrix of an array. Additionally, {wi(n)} are temporally and spatially complex white Gaussian noise which are uncorrelated each other and has zero-mean and variance σ2. Here, the array covariance matrix is expressed as below,R=E{y(n)yH(n)}=ARsAH+σ2IM  [Equation 2]where E{•} and (•)H express an expectation operation and a complex conjugate transpose, respectively, Rs=E{s(n)SH(n)} is the covariance matrix of an incident signals, IM is an M×M identity matrix. Further, when the correlation rik of the observation data yi(n) and yk(n) is defined by rik=E{yi(n)yk*(n)}, the above array covariance matrix R can be explicitly expressed by a formula below,
                    R        =                  [                                                                      r                  11                                                                              r                  12                                                            …                                                              r                                      1                    ⁢                    M                                                                                                                        r                  21                                                                              r                  22                                                            …                                                              r                                      2                    ⁢                    M                                                                                                      ⋮                                            ⋮                                            ⋰                                            ⋮                                                                                      r                  M1                                                                              r                  M2                                                            …                                                              r                  MM                                                              ]                                    [                  Equation          ⁢                                          ⁢          3                ]            where rik=r*ik, and (•)* expresses the complex conjugate.
FIG. 1 explains the dividing of the uniform linear array into subarrays.
In the spatial smoothing based MUSIC, in order to estimate the arrival directions {θk} of fully correlated signals (i.e., coherent signals or multipath waves), the entire uniform linear array is divided into L overlapped subarrays consisting of m elements (where 1≦m≦M) as shown in FIG. 1, where m and L are the subarray size and the number of subarrays, respectively, and L=M−m+1 is satisfied. Based on the equation 1, the signal vector y1(n) of the lth subarray can be expressed by equation 4 as below,y1(n)=[y1(n),yl+1(n), . . . ,yl+m−1(n‘)]T=Am Dl−1s(n)+w1(n)   [Equation 4]where Am=[am(θ1), am(θ2), . . . am(θp)] am(θk)=[l,ejω0r(θk), . . . , ejω0(m−1)r(θk)]T, wl(n)=[wl(n), wl+1 (n), . . . , wl−m+1(n)]T, D is a diagonal matrix with the elements ejω0r(θ1), ejω0r(θ2), . . . , ejω0(m−1)r(θp), and l=1, 2, . . . , L. Also, am (θk) and Am are the array response vector and response matrix of a subarray, respectively. Accordingly, the covariance matrix of the 1th subarray can be expressed by equation 5 asRl=E{y1(n)y1H(n)}=AmDl−1Rs(Dl−1)Am H+σ2Im   [Equation 5]Further, by spatially averaging the covariance matrixes {Ri} of L subarrays, the spatially averaged covariance matrix is obtained
                              R          _                =                              1            L                    ⁢                                    ∑                              l                =                1                            L                        ⁢                                                  ⁢                          R              l                                                          [                  Equation          ⁢                                          ⁢          6                ]            Then the eigenvalue decomposition of the above spatially averaged covariance matrix {overscore (R)} can be expressed by formula 7 as below,
                              R          _                =                                            ∑                              i                =                1                            m                        ⁢                                                  ⁢                                          λ                i                            ⁢                              e                i                            ⁢                              e                i                H                                              =                      E            ⁢                                                  ⁢            Λ            ⁢                                                  ⁢                          E              H                                                          [                  Equation          ⁢                                          ⁢          7                ]            where ei and λi are the eigenvector and eigenvalue of the matrix {overscore (R)}, respectively, E is the eigenvector matrix with {ei} as a column, Λ is a diagonal matrix with the element {λi}. Also, the space spanned by the eigenvectors {e1, e2, . . . , ep} is called the signal subspace, and the space spanned by the vectors {ep+1, ep+2, . . . , em} is called the noise subspace. Further, the signal subspace can be expressed by using the array response vector. The method for direction estimation based on the orthogonality between the signal subspace and the noise subspace is called a subspace-based method.
From the eigenvalue analysis of the covariance matrix {overscore (R)} expressed by the equation 7, the orthogonality is established between the array response vector am(θk) of the subarray and the eigenvector {ep, ep+1, . . . , em} as expressed by equation 8 as beloweiHam(θk)=0   [Equation 8]where i=p+1, . . . , m. Based on the above orthogonality, the spectrum {overscore (P)}ssmusic(θ) as below can be calculated,
                                                        P              _                        ssmusic                    ⁡                      (            θ            )                          =                  1                                    ∑                              i                =                                  p                  +                  1                                            m                        ⁢                                                  ⁢                                                                                                e                    i                    H                                    ⁢                                                            a                      m                                        ⁡                                          (                      θ                      )                                                                                                  2                                                          [                  Equation          ⁢                                          ⁢          9                ]            where am(a)=[1,ejω0r(θ), . . . , ejω0(m−1)r(θ)]T. In the spatial smoothing based MUSIC, the directions of incident signals is estimated based on the position of the p highest peaks of the spectrum given by equation 7.
As shown in equation 7, the subspace-based method for estimating the directions of incident signals, such as the (spatial smoothing based) MUSIC requires the eigenvalue decomposition of the array covariance matrix in order to obtain the signal subspace or the noise subspace. However, for a real installed array antenna, especially in the case where the number of array elements is larger or the varying arrival directions should be estimated in a on-line manner, the process of the eigenvalue decomposition (or the singular value decomposition) becomes computationally complex so that much time is required for the calculation. Accordingly, the applications of the conventional subspace-based direction estimation method with eigendecomposition are limited in the actual situations by the heavy computational load of the eigendecomposition process. Further, if the direction of signals incident on the array is not estimated quickly and accurately, the receiving/transmitting beam of the base station cannot be formed accurately, and then the performance of the receiving and transmitting system of the base station will degrade.